Intro to Statistics: Population, Sampling, and Distribution Concepts

Population

The entire group being studied.

Sample

A subset used to represent a population.

Parameter

Describes a population.

Statistic

Describes a sample.

Descriptive Statistics

Summarizes data.

Inferential Statistics

Makes predictions about a population.

Construct

An abstract concept.

Operational Definition

Explains how a construct is measured.

Discrete Variables

Countable variables.

Continuous Variables

Measurable variables.

Scales of Measurement

Nominal, ordinal, interval, ratio.

Correlational Methods

Measures relationships.

Experimental Methods

Manipulates variables to find cause.

Characteristics of a Distribution

Shape, central tendency, and variability.

Symmetrical Distribution

Balanced distribution.

Skewed Distribution

Distribution with a tail on one side (positive or negative).

Measures of Central Tendency

Mean, median, mode.

Median

Used instead of mean when the data is skewed.

Standard Deviation Formula

Provided on your exam—know how to apply it to population vs. sample.

Effect of Adding/Multiplying on SD

Adding/subtracting doesn't change SD; multiplying/dividing scales it.

Probability Formula

P(A)=favorable outcomes/total outcomes.

Random Sampling

Determines who's in the study.

Random Assignment

Determines who gets which condition.

Z-Score

A standardized score showing how far a value is from the mean.

Z-Score Formula

z=x−μ/σ.

Unit Normal Table

Shows the proportion of scores below a given z-score.

Finding Probability Using Z-Score

Convert to z, then use the table to find the area under the curve.

Distribution of Sample Means

The distribution of means from all possible samples of a given size.

Central Limit Theorem

As sample size increases, the distribution of sample means becomes normal.

Expected Value of M

It equals the population mean μ.

Standard Error Formula

σM=σ/√n.

Law of Large Numbers

Larger samples produce means closer to the population mean.

Finding Probability of a Sample Mean

Use z=M−μ/σM, then check the unit normal table.